A force field is described by $< F_{x}, F_{y}, F_{z} > = < x + y, 2 z, 2 y - z >$ $<F_x,F_y,F_z> = < x +y , 2z, 2y -z >$ . Is this force field conservative?

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Answer 1 · 2016-06-07T16:06:29

The force field is not conservative bacause $- \to \nabla \times \to F \neq \to 0$ $vec grad xx vec F ne vec 0$

Calculating the force field curl we have

$((hat i, hat j, hat k), (partial/(partial x),partial/(partial y), partial/(partial z)), (x+y,2z,2y-z)) = (0,0,-hat k)$

which is different from $vec 0$

A force field is described by <F_x,F_y,F_z> = < x +y , 2z, 2y -z > <Fx,Fy,Fz>=<x+y,2z,2y−z><F_x,F_y,F_z> = < x +y , 2z, 2y -z > . Is this force field conservative?